# How to calculate the following limit - I'm stuck!

1. Jan 4, 2009

### chemic_23

1. The problem statement, all variables and given/known data

what is the limit of as x approaches 9?

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 4, 2009

### sara_87

Re: factoring

I would do it this way:
remember that:
a$$^{2}$$-b$$^{2}$$=(a+b)(a-b)
so
a-b=$$\frac{(a^2-b^2}{(a+b)}$$

so take the numerator and denominator of your problem and treat each as a-b
so:
$$\sqrt{x}-3$$ = $$\frac{x-9}{\sqrt{x}+3}$$ (1)

and
$$\sqrt{1+\sqrt{x}}-2$$ = $$\frac{\sqrt{x} - 3}{\sqrt{1+\sqrt{x}}+2}$$ (2)

so your limit is now (1)/(2): which gives:

$$\frac{x-9}{\sqrt{x}+3}\times\frac{\sqrt{1+\sqrt{x}}+2}{\sqrt{x}-3}$$

Is this clear?
Do you know how to continue from here?

3. Jan 4, 2009

### chemic_23

Re: factoring

continuation...

thus, the limit of as x approaches 9 is 4. Is this correct?

4. Jan 4, 2009

### Dick

Re: factoring

Correct.